type 7 finding sum difference product based ratio & proportion problems Practice Questions Answers Test with Solutions & More Shortcuts

Question : 16 [SSC CHSL 2012]

The total number of students in a school was 660. The ratio between boys and girls was 13 : 9. After some days, 30 girls joined the school and some boys left the school and new ratio between boys and girls became 6 : 5. The number of boys who left the school is :

a) 30

b) 60

c) 40

d) 50

Answer: (a)

In the first case,

Boys = $660 × 13/22$ = 390

Girls = $660 × 9/22$ = 270

If x boys leave the school, then

${390 - x}/{270 + 30} = 6/5$

390 - x = 360

x = 390 - 360 = 30

Question : 17 [SSC CPO S.I.2006]

The ratio of the number of ladies to that of gents at a party was 3 : 2. When 20 more gents joined the party, the ratio was reversed. The number of ladies present at the party was

a) 24

b) 16

c) 32

d) 36

Answer: (a)

Let the number of ladies and gents be 3x and 2x respectively.

According to the question,

${3x}/{2x + 20} = 2/3$

9x = 4x + 40

5x = 40 ⇒ x = 8

Number of ladies = 3x

= 3 × 8 = 24

Question : 18 [SSC CGL Tier-I 2013]

Three numbers are in the ratio 1 : 2 : 3. By adding 5 to each of them, the new numbers are in the ratio 2 : 3 : 4. The numbers are:

a) 1, 2, 3

b) 5, 10, 15

c) 15, 30, 45

d) 10, 20, 30

Answer: (b)

Numbers = x, 2x and 3x

${x + 5}/{2x + 5}= 2/3$

4x + 10 = 3x + 15

x = 5

Numbers = 5, 10 and 15

Question : 19 [SSC CGL Prelim 2002]

The students in three classes are in the ratio 2 : 3 : 5. If 40 students are increased in each class, the ratio changes to 4 : 5 : 7. Originally, the total number of students was :

a) 200

b) 400

c) 180

d) 100

Answer: (a)

Let the number of students in three classes be 2x, 3x and 5x respectively.

Due to increase of 40 students in each class,

we have ${2x + 40}/{3x + 40} = 4/5$

10x + 200 = 12x + 160

2x = 200 - 160

2x = 40 ⇒ x = 20

Original strength

= 10x = 10 × 20 = 200

Question : 20 [SSC CGL Tier-I 2010]

What must be added to each term of the ratio 7 : 11, so as to make it equal to 3 : 4 ?

a) 6.5

b) 5

c) 7.5

d) 8

Answer: (b)

Let the required number be x.

${7 + x}/{11 + x} = 3/4$

28 + 4x = 33 + 3x

x = 33 - 28 = 5

IMPORTANT quantitative aptitude EXERCISES

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